Abstract

A hyperspectral Shack–Hartmann test bed has been developed to characterize the performance of miniature optics across a wide spectral range, a necessary first step in developing broadband achromatized all-polymer endomicroscopes. The Shack–Hartmann test bed was used to measure the chromatic focal shift (CFS) of a glass singlet lens and a glass achromatic lens, i.e., lenses representing the extrema of CFS magnitude in polymer elements to be found in endomicroscope systems. The lenses were tested from 500 to 700nm in 5 and 10nm steps, respectively. In both cases, we found close agreement between test results obtained from a ZEMAX model of the test bed and test lens and those obtained by experiment (maximum error of 12μm for the singlet lens and 5μm for the achromatic triplet lens). Future applications of the hyperspectral Shack–Hartmann test include measurements of aberrations as a function of wavelength, characterization of manufactured plastic endomicroscope elements and systems, and reverse optimization.

Best-performing achromatic doublet designed using optical-polymer materials (PMMA and PS). The lens diameter is 3mm and the total lens thickness is 4.1mm. A.S., aperture stop. Part (b) shows the chromatic focal shift for the doublet design of (a). See text for details.

Schematic representation of the hyperspectral Shack–Hartmann test bed. The inset illustrates how wavefront deformations in the exit pupil of the lens (or system) under test are converted to lenslet focal-spot displacements.

Black box representing the size of a single pixel (5.2μm×5.2μm) in our camera. Blue crosses represent the focal-spot centroids calculated for a series of 200 sequential measurements from a single lenslet at a fixed test-lens position and fixed wavelength. Noise in the system contributes to reduced precision of the centroid calculation. These centroids are averaged together to produce a single centroid location for this lenslet at this wavelength, which will then be processed with the Shack– Hartmann analysis software.

Predicted and measured hyperspectral Shack–Hartmann test results. Part (a) compares the predicted spectral change in focal length for a singlet lens to experimental measurements with the hyperspectral Shack–Hartmann test. Part (b) compares the predicted spectral change in focal length for a triplet achromatic lens to experimental measurements with the hyperspectral Shack–Hartmann test. Note the change in the ordinate-axis scale between Parts (a) and (b). See text for details.

Equations (1)

Metrics

Table 1

Design Parameters for the PMMA and Polystyrene (PS) Doublet (See Text for Details)

Surface number

Radius of curvature [mm]

Thickness [mm]

Material

Semidiameter [mm]

Conic

1

2.67

1.1

PMMA

1.5

−0.12

2

−2.10

3.0

PS

1.5

3

−5.18

6.63

Table 2

Optical and Mechanical Properties of PMMA and Polystyrene Used to Create the Achromatized Doubleta

n(435.8nm)

n(587.6nm)

n(703nm)

Abbe Number

Coefficient of Thermal Expansion

Water Absorption

Polystyrene (Rexoliate 1422)

1.617

1.592

1.582

30.5

7.0⋅10−5/°C

0.08% Max

PMMA

1.502

1.491

1.486

59.2

5–10⋅10−5/°C

0.1–0.5%

a The water absorption column specifies a percent increase in the weight of the plastic after a time and amount of water specified by the ASTM D570 test. This factor is important in endomicroscopy, since an optical element might be exposed to aqueous environments when inserted into the body.

Table 3

Overview of Verification Method Trade-Offs (See Text for Details)

Interferometry

Image Evaluation

Shack–Hartmann Test

Hyperspectral

•

•

Able to test nonspherical object without null surface

•

•

Can measure multiple aberrations

•

•

Commercial off-the-shelf equipment and minimal setup labor

•

•

Highly sensitive

•

•

Tables (3)

Table 1

Design Parameters for the PMMA and Polystyrene (PS) Doublet (See Text for Details)

Surface number

Radius of curvature [mm]

Thickness [mm]

Material

Semidiameter [mm]

Conic

1

2.67

1.1

PMMA

1.5

−0.12

2

−2.10

3.0

PS

1.5

3

−5.18

6.63

Table 2

Optical and Mechanical Properties of PMMA and Polystyrene Used to Create the Achromatized Doubleta

n(435.8nm)

n(587.6nm)

n(703nm)

Abbe Number

Coefficient of Thermal Expansion

Water Absorption

Polystyrene (Rexoliate 1422)

1.617

1.592

1.582

30.5

7.0⋅10−5/°C

0.08% Max

PMMA

1.502

1.491

1.486

59.2

5–10⋅10−5/°C

0.1–0.5%

a The water absorption column specifies a percent increase in the weight of the plastic after a time and amount of water specified by the ASTM D570 test. This factor is important in endomicroscopy, since an optical element might be exposed to aqueous environments when inserted into the body.